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The de Broglie wavelength ( $λ$ ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v₀ is threshold freqency]

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lambda propto frac{1}{{{(v-{{v}_{0}})}^{frac{3}{2}}}}

lambda propto frac{1}{{{(v-{{v}_{0}})}^{frac{1}{2}}}}

lambda propto frac{1}{{{(v-{{v}_{0}})}^{frac{1}{4}}}}

answer is B.

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Detailed Solution

KE of photoelectrons
KE $=hupsilon -h{{upsilon }_{0}}$ ... (1)

$lambda =frac{h}{sqrt{2mKE}}$ ... (2)

substituting 1 in 2

$lambda ={frac{h}{sqrt 2mhleft( v-{{v}_{0}} right)}}$ ( $therefore$ h, m are constants)

$Rightarrow lambda propto frac{1}{{{left( v-{{v}_{0}} right)}^{frac{1}{2}}}}$

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